Answer is: the dosage of quinine is equivalent to 3040,9 μg/kg.
first convert ib (pounds) to kg (kilograms):
1 pound (lb) is equal to 0,45359237 kilograms (kg).
145 ib = 145 ib · 0,45359237 kg/ib = 65,77 kg.
second - convert milligrams (mg) to micrograms (μg):
1 milligram (mg) is equal to 1000 μg.
200 mg = 200 mg · 1000 μg/mg = 200000 μg = 2×10⁵ μg.
third - the ratio is 200000 μg / 65,77 kg = 3040,9 μg/kg.